Fluid pumping of peristaltic vessel fitted with elastic valves

Wolf, K. T.; Dixon, J. Brandon; Alexeev, Alexander

doi:10.1017/jfm.2021.302

Cited by 9 publications

(27 citation statements)

References 80 publications

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“…A 3D finite-element FSI model with all structural parts made flexible was achieved for the first time by Bertram [ 19 ]; the model showed how the degree of bias of the valve characteristics to the open position increased with the inter-leaflet gap in the resting position and with valve inflation pressure. A different fluid–structure approach, involving application of the lattice-Boltzmann technique, was taken by Alexeev and Dixon [ 20 , 21 ], after the pioneering work of Buxton and Clarke [ 22 ] for vein valves. The method seems to provide unparalleled ability to model leaflets of extreme flexibility.…”

Section: Introductionmentioning

confidence: 99%

An Enhanced 3D Model of Intravascular Lymphatic Valves to Assess Leaflet Apposition and Transvalvular Differences in Wall Distensibility

Bertram

Davis

2023

Biology

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Lymphatic valves operate in a fluid-dynamically viscous environment that has little in common with that of cardiac valves, and accordingly have a different, axially lengthened, shape. A previously developed 3D fluid/structure interaction model of a lymphatic valve was extended to allow the simulation of stages of valve closure after the leaflets come together. This required that the numerical leaflet be prevented from passing into space occupied by the similar other leaflet. The resulting large deflections of the leaflet and lesser deflections of the rest of the valve were mapped as functions of the transvalvular pressure. In a second new development, the model was reconstructed to allow the vessel wall to have different material properties on either side of where the valve leaflet inserts into the wall. As part of this, a new pre‑processing scheme was devised which allows easier construction of models with modified valve dimensions, and techniques for successfully interfacing the CAD software to the FE software are described. A two-fold change in wall properties either side of the leaflet made relatively little difference to valve operation apart from affecting the degree of sinus distension during valve closure. However, the numerically permitted strains were modest (<14%), and did not allow examination of the large-scale highly nonlinear elastic properties exhibited by real lymphatic vessels. A small series of murine popliteal, mesenteric, and inguinal-axillary lymphatic vessel segments containing a valve were experimentally investigated ex vivo. The pressure–diameter curves measured just upstream and just downstream of the valve were parameterised by computing the difference in tubular distensibility at three values of transmural pressure. In the popliteal and mesenteric segments, it was found that the distensibility was usually greater just downstream, i.e., in the sinus region, than upstream, at low and intermediate transmural pressure. However, there was wide variation in the extent of difference, and possible reasons for this are discussed.

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Section: Introductionmentioning

confidence: 99%

An Enhanced 3D Model of Intravascular Lymphatic Valves to Assess Leaflet Apposition and Transvalvular Differences in Wall Distensibility

Bertram

Davis

2023

Biology

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“…We model the three-dimensional fluid flow in lymphatic vessels using a lattice Boltzmann model (LBM) that recovers the Navier-Stokes equations. LBM ability to efficiently simulate flows in problems with moving walls gives this method a great advantage in modeling the intrinsic pumping in lymphatic system [35]. In LBM, the time evolution of the distribution function of the fluid 'particles' is evaluated.…”

Section: Methodsmentioning

confidence: 99%

“…The method of momentum exchange combined with the interpolated bounce-back rule is used to ensure momentum-conserving two-way coupling at the fluid-solid boundaries [37,42]. We have previously extensively validated our FSI approach including simulations of lymphatic vessels [35,43].…”

Section: Methodsmentioning

confidence: 99%

“…We have recently developed a three-dimensional, fully-coupled FSI model to investigate the behavior of compliant lymphatic valves in a static cylindrical vessel [34] and in a vessel that undergoes peristaltic contractions [35]. The simulations demonstrated the dependence of the lymphatic vessel pumping on the geometric features and mechanical properties of valve and the vessel contraction parameters such as contraction wave speed and amplitude.…”

Section: Introductionmentioning

confidence: 99%

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Effect of valve spacing on peristaltic pumping

et al. 2023

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Peristaltic fluid pumping due to a periodic contraction wave in a vessel fitted with one-way elastic valves is investigated numerically. It is concluded that the valve spacing within the vessel relative to the contraction wavelength plays a critical role in providing efficient pumping. When the valve spacing does not match the wavelength, the valves open asynchronously and the volume of the vessel segments bounded by two consecutive valves changes, thereby inducing volumetric fluid pumping. The volumetric pumping leads to higher pumping flowrate and efficiency against an adverse pressure gradient. The optimum pumping occurs when the ratio of valve spacing to contraction wavelength is about 2⁄3. This pumping regime is characterized by a longer period during which the valves are open. The results are useful for further understanding the pumping features of lymphatic system and provide insight into the design of biomimetic pumping devices.

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“…This is equivalent to the diode representation of valves used in lumped models of the lymphatic system [9]. A more detailed valve model could incorporate the mechanical properties of the valves such as the bending and stretching stiffness [17]. Superscripts are used to index a particular valve; specifically, x𝑖 𝑣 is used to denote the position of valve 𝑖, while 𝜖 refers to the separation distance between valves in units of 𝜆.…”

Section: Incorporating Valves Into a Model For Peristalsismentioning

confidence: 99%

Operating Principles of Peristaltic Pumping through a Dense Array of Valves

Winn¹,

Katifori²

2021

Preprint

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Immersed nonlinear elements are prevalent in biological systems that require a preferential flow direction. A certain class of models is investigated where the fluid is driven by peristaltic pumping and the nonlinear elements are ideal valves that completely suppress backflow. This highly nonlinear system produces discontinuous solutions that are difficult to study. As the density of valves increases, the pressure and flow are well-approximated by a continuum of valves which can be analytically treated. Interestingly, two different pumping mechanisms emerge from this model. At low frequencies, diffusive transport pushes open all but one valve, and the radius takes the shape of the imposed force. At high frequencies, half of the valves open, and the flow is determined by the advective transport induced by peristalsis. In either case, the induced flow is linear in the amplitude of the peristaltic forces and is independent of pumping direction. Despite the continuum approximation used, the physical valve density is accounted for by modifying the resistance of the fluid appropriately. The suppression of backflow causes a net benefit in adding valves when the valve density is low, but once the density is high enough, the dominant valve effect is to suppress the forward flow, suggesting there is an optimum number of valves per wavelength.FIG. 1. Model for peristaltic pumping with many valves satisfying the assumption (1).

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Fluid pumping of peristaltic vessel fitted with elastic valves

Abstract: Abstract

Cited by 9 publications

References 80 publications

An Enhanced 3D Model of Intravascular Lymphatic Valves to Assess Leaflet Apposition and Transvalvular Differences in Wall Distensibility

An Enhanced 3D Model of Intravascular Lymphatic Valves to Assess Leaflet Apposition and Transvalvular Differences in Wall Distensibility

Effect of valve spacing on peristaltic pumping

Operating Principles of Peristaltic Pumping through a Dense Array of Valves

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